Asta-Advances in Statistical Analysis最新文献

A common choice for the marginal distribution of a bivariate count time series is the bivariate Poisson distribution. In practice, however, when the count data exhibit zero inflation, overdispersion or non-stationarity features, such that a marginal bivariate Poisson distribution is not suitable. To test the discrepancy between the actual count data and the bivariate Poisson distribution, we propose a new goodness-of-fit test based on a bivariate dispersion index. The asymptotic distribution of the test statistic under the null hypothesis of a first-order bivariate integer-valued autoregressive model with marginal bivariate Poisson distribution is derived, and the finite-sample performance of the goodness-of-fit test is analyzed by simulations. A real-data example illustrate the application and usefulness of the test in practice.

In this paper, we propose a Bayesian quantile regression (QR) approach to jointly model multivariate ordinal data. Firstly, a multivariate latent variable model is used to link the multivariate ordinal data and latent continuous responses and the multivariate asymmetric Laplace (MAL) distribution is employed to construct the joint QR-based working likelihood for the considered model. Secondly, adaptive-(L_{1/2}) penalization priors of regression parameters are incorporated into the working likelihood to implement high-dimensional Bayesian joint QR inference. Markov Chain Monte Carlo (MCMC) algorithm is utilized to derive the fully conditional posterior distributions of all parameters. Thirdly, Bayesian joint relatively QR estimation approach is recommended to result in more efficient estimation results. Finally, Monte Carlo simulation studies and a real instance analysis of multirater agreement data are presented to illustrate the performance of the proposed Bayesian joint relatively QR approach.

This paper focuses on the general linear measurement error model, in which some or all predictors are measured with error, while others are measured precisely. We propose a semi-parametric estimator that works under general mechanisms of measurement error, including differential and non-differential errors. Other popular methods, such as the corrected score and conditional score methods, only work for non-differential measurement error models, but our estimator works in all scenarios. We develop our estimator by considering a family of objective functions that depend on an unspecified weight function. Using statistical error analysis and perturbation theory, we derive the optimal weight function under the small-sigma regime. The resulting estimator is statistically optimal in all senses. Even though we develop it under the small-sigma regime, we also establish its consistency and asymptotic normality under the large sample regime. Finally, we conduct a series of numerical experiments to confirm that the proposed estimator outperforms other existing methods.

Benford’s law is a particular discrete probability distribution that is often satisfied by the significant digits of a dataset. The nonconformity with Benford’s law suggests the possible presence of data manipulation. This paper introduces two novel generalized versions of Benford’s law that are less restrictive than the original Benford’s law—hence, leading to more probable conformity of a given dataset. Such generalizations are grounded on the existing mathematical relations between Benford’s law probability distribution elements. Moreover, one of them leads to a set of probability distributions that is a proper subset of that of the other one. We show that the considered versions of Benford’s law have a geometric representation on the three-dimensional Euclidean space. Through suitable optimization models, we show that all the probability distributions satisfying the more restrictive generalization exhibit at least acceptable conformity with Benford’s law, according to the most popular distance measures. We also present some examples to highlight the practical usefulness of the introduced devices.

We propose to investigate the joint dynamics of regional gross domestic product and life expectancy in Italy through Wasserstein barycenter regression derived from optimal transport theory. Wasserstein barycenter regression has the advantage of being flexible in modeling complex data distributions, given its ability to capture multimodal relationships, while maintaining the possibility of incorporating uncertainty and priors, other than yielding interpretable results. The main findings reveal that regional clusters tend to emerge, highlighting inequalities in Italian regions in economic and life expectancy terms. This suggests that targeted policy actions at a regional level fostering equitable development, especially from an economic viewpoint, might reduce regional inequality. Our results are validated by a robustness check on a human mobility dataset and by an illustrative forecasting exercise, which confirms the model’s ability to estimate and predict joint distributions and produce novel empirical evidence.